We investigate whether the spin or charge degrees of freedom are responsible for the nodal gap in underdoped cuprates by performing inelastic neutron scattering and x-ray diffraction measurements on ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, which is on the edge of the antiferromagnetic phase. We found that a fluctuating incommensurate spin-density wave (SDW) with a bottom part of an hourglass dispersion exists even in this magnetic sample. The strongest component of these fluctuations diminishes at the same temperature where the nodal gap opens. X-ray scattering measurements on the same crystal show no signature of a charge-density wave (CDW). Therefore, we suggest that the nodal gap in the electronic band of this cuprate opens due to fluctuating SDW with no contribution from CDW.

It is now well established that superconducting cuprates support a charge-density-wave state in the so-called underdoped region of their phase diagram. We investigate the possibility of charge order in the square-lattice Hubbard model, both alone and in coexistence with $d$-wave superconductivity. The charge order has a period of 4 in one direction, is centered on bonds, and has a $d$ form factor. We use the variational cluster approximation, an approach based on a rigorous variational principle that treats short-range correlations exactly, with two clusters of size $2\times 6$ that together tile the infinite lattice and provide a nonbiased unit for a period-4 bond-density wave (BDW). We find that the BDW exists in a finite range of hole doping and increases in strength from $U=5$ to $U=8$. Its location and intensity depend strongly on the band dispersion. When probed simultaneously with $d$-wave superconductivity, the energy is sometimes lowered by the presence of both phases, depending on the interaction strength. Whenever they coexist, a pair-density wave (a modulation of superconducting pairing with the same period and form factor as the BDW) also exists.

We argue that a particle language provides a conceptually simple framework for the description of anomalous equilibration in isolated quantum systems. We address this paradigm in the context of integrable models, which are those where particles scatter completely elastically and are stable against decay. In particular, we demonstrate that a complete description of equilibrium ensembles for interacting integrable models requires a formulation built from the mode occupation numbers of the underlying particle content, mirroring the case of noninteracting particles. This yields an intuitive physical interpretation of generalized Gibbs ensembles, and reconciles them with the microcanonical ensemble. We explain how previous attempts to identify an appropriate ensemble overlooked an essential piece of information, and provide explicit examples in the context of quantum quenches.

Optomechanical crystals, purposely designed and fabricated semiconductor nanostructures, are used to enhance the coupling between the electromagnetic field and the mechanical vibrations of matter at the nanoscale. However, in real optomechanical crystals, imperfections open extra channels where the transfer of energy is lost, reducing the optomechanical coupling efficiency. Here, we quantify the role of disorder in a paradigmatic one-dimensional optomechanical crystal with full phononic and photonic band gaps. We show how disorder can be exploited as a resource to enhance the optomechanical coupling beyond engineered structures, thus providing a new tool set for optomechanics.

In this work we report a theoretical investigation on behavior of the elastic constant ${\mathrm{C}}_{44}$ and the transverse optical phonon mode ${\mathrm{E}}_{2g}$ of $\alpha$-Hf under pressure within the density functional theory. In contrast to many other reported transition metals, the above two quantities do not show a synchronous relation as pressure increases. Below 13 GPa, an opposite shifting tendency has been observed. However, once the pressure is raised above 13 GPa, the trend is pulled back to be consistent. This anomalous behavior is figured out to be caused by the large lattice anisotropy of the $c/a$ ratio along with the elastic anisotropy. The synchronous behavior is found to be in accordance with the behavior of $c/a$ ratio with increased pressure. In our band-structure investigations the electronic topological transition has been discovered at 10 GPa, which relates to the change of $c/a$ ratio suggested by recent literature. The presence of the Van Hove singularity shown in the densities of states has been identified and regarded as the origin of the variation of ${\mathrm{C}}_{44}$ and ${\mathrm{E}}_{2g}$.

The diagonal ensemble is the infinite time average of a quantum state following unitary dynamics in systems without degeneracies. In analogy to the time average of a classical phase-space dynamics, it is intimately related to the ergodic properties of the quantum system giving information on the spreading of the initial state in the eigenstates of the Hamiltonian. In this work we apply a concept from quantum information, known as total correlations, to the diagonal ensemble. Forming an upper bound on the multipartite entanglement, it quantifies the combination of both classical and quantum correlations in a mixed state. We generalize the total correlations of the diagonal ensemble to more general $\alpha$-Renyi entropies and focus on the cases $\alpha =1$ and $\alpha =2$ with further numerical extensions in mind. Here we show that the total correlations of the diagonal ensemble is a generic indicator of ergodicity breaking, displaying a subextensive behavior when the system is ergodic. We demonstrate this by investigating its scaling in a range of spin chain models focusing not only on the cases of integrability breaking but also emphasize its role in understanding the transition from an ergodic to a many-body localized phase in systems with disorder or quasiperiodicity.

The theory of spin drift and diffusion in two-dimensional electron gases is developed in terms of a random walk model incorporating Rashba, linear and cubic Dresselhaus, and intersubband spin-orbit couplings. The additional subband degree of freedom introduces new characteristics to the persistent spin helix (PSH) dynamics. As has been described before, for negligible intersubband scattering rates, the sum of the magnetization of independent subbands leads to a checkerboard pattern of crossed PSHs with long spin lifetime. For strong intersubband scattering we model the fast subband dynamics as a new random variable, yielding a dynamics set by averaged spin-orbit couplings of both subbands. In this case the crossed PSH becomes isotropic, rendering circular (Bessel) patterns with short spin lifetime. Additionally, a finite drift velocity breaks the symmetry between parallel and transverse directions, distorting and dragging the patterns. We find that the maximum spin lifetime shifts away from the PSH regime with increasing drift velocity. We present approximate analytical solutions for these cases and define their domain of validity. Effects of magnetic fields and initial package broadening are also discussed.

Since the ionization potential (IP) is one of the fundamental quantities in a solid, ruling the physical and chemical properties and electronic device performances, many researchers have quantified the IPs using first-principles calculations of slab models recently. However, the breakdown into bulk and surface contributions has remained a contentious issue. In this study, we discuss how to decompose the IP into the bulk and surface contributions by using the macroscopic average technique. Although this procedure quantifies well-defined macroscopic dipoles and corroborates with the continuous model, it is not consistent with the physical intuition. This is because the strong charge fluctuation inside solids significantly contributes to the macroscopic dipole potential. We also discuss the possibility of an alternative splitting procedure that can be consistent with the physical intuition, and conclude that it is possible only when both bulk and surface charge density is well decomposed into a superposition of spherical charges. In the latter part, we evaluate the IPs of typical semiconductors and insulators such as Si, diamond, GaAs, GaN, ZnO, and MgO, using atomic-charge and molecular-charge approximations, in which the charge density of a solid is described as a superposition of charge density of the constituent atoms and molecules, respectively. We find that the atomic-charge approximation also known as the model-solid theory can successfully reproduce the IPs of covalent materials, but works poorly for ionic materials. On the other hand, the molecular-charge approximation, which partly takes into account the charge transfer from cations to anions, shows better predictive performance overall.

Electronic structures and transport properties of graphene on $h$-BN with carbon impurities are investigated by first-principles calculation and the tight-binding model. We show that the coupling between the impurity level and the graphene's Dirac cone sensitively depends on the impurity position, and in particular, it nearly vanishes when the impurity is located right below the center of the six membered ring of graphene. The Bloch phase factor at the Brillouin zone edge plays a decisive role in the cancellation of the hopping integrals. The impurity position dependence on the electronic structures of graphene on $h$-BN is investigated by the first-principles calculation, and its qualitative feature is well explained by a tight-binding model with graphene and a single impurity site. We also propose a simple one-dimensional chain-impurity model to analytically describe the role of the quantum interference in the position-dependent coupling.

We describe a classical thermodynamic model that reproduces the main features of the solid hydrogen phase diagram. In particular, we show how the general structure types, which are found by electronic structure calculations and the quantum nature of the protons, can also be understood from a classical viewpoint. The model provides a picture not only of crystal structure, but also for the anomalous melting curve and insights into isotope effects, liquid metallisation, and infrared activity. The existence of a classical picture for this most quantum of condensed matter systems provides a surprising extension of the correspondence principle of quantum mechanics, in particular the equivalent effects of classical and quantum uncertainty.

We show that single-crystal, equiatomic solid solutions of Lennard-Jones particles have a plurality of inherent states: mechanically stable configurations with identical lattice site occupancies, yet distinct potential-energy minima. External loading triggers transitions between inherent states via localized shear transformations. A plurality of inherent states and mechanically activated transitions between them make equiatomic solid solutions an unusual form of matter: one that is crystalline like single-component metals, yet exhibits localized shear transformations like metallic glasses.

This work discloses a surprising, previously unknown heterogeneous growth mode. Namely, large-area, thin sheets of single-crystalline Ge were observed to grow laterally on top of a polycrystalline Al substrate, covering as many as tens of differently oriented Al grains at low temperatures. The observation of the Ge crystal-growth process by in situ heating transmission electron microscopy demonstrates an intriguing type of “faceted” growth: the growth of single-crystalline Ge thin sheets proceeding Al-grain by Al-grain on top of the polycrystalline Al substrate. The crystalline Ge growth front tends to align along the lines of intersection of the Al grain boundaries with the Al surface. Such an unusual heterogeneous growth mode has been shown to be a consequence of the strong anisotropy of the energy of the crystalline/crystalline (here: c-Ge/c-Al) interfaces.

Acoustic topological states support sound propagation along the boundary in a one-way direction with inherent robustness against defects and disorders, leading to the revolution of the manipulation on acoustic waves. A variety of acoustic topological states relying on circulating fluid, chiral coupling, or temporal modulation have been proposed theoretically. However, experimental demonstration has so far remained a significant challenge, due to the critical limitations such as structural complexity and high losses. Here, we experimentally demonstrate an acoustic anomalous Floquet topological insulator in a waveguide network. The acoustic gapless edge states can be found in the band gap when the waveguides are strongly coupled. The scheme features simple structure and high-energy throughput, leading to the experimental demonstration of efficient and robust topologically protected sound propagation along the boundary. The proposal may offer a unique, promising application for design of acoustic devices in acoustic guiding, switching, isolating, filtering, etc.

We investigate doping- and pressure-induced changes in the electronic state of Mn $3d$ and As $4p$ orbitals in II-II-V-based diluted magnetic semiconductor $\left(\mathrm{B}{\mathrm{a}}_{1-x}{\mathrm{K}}_x\right){\left(\mathrm{Z}{\mathrm{n}}_{1-y}\mathrm{M}{\mathrm{n}}_y\right)}_2\mathrm{A}{\mathrm{s}}_2$ to shed light into the mechanism of indirect exchange interactions leading to high ferromagnetic ordering temperature ($T\mathrm{c}=230\mathrm{K}$ in optimally doped samples). A suite of x-ray spectroscopy experiments (emission, absorption, and dichroism) show that the emergence and further enhancement of ferromagnetic interactions with increased hole doping into the As $4p$ band is accompanied by a decrease in local $3d$ spin density at Mn sites. This is a result of increasing Mn $3d–\mathrm{As} 4p$ hybridization with hole doping, which enhances indirect exchange interactions between Mn dopants and gives rise to induced magnetic polarization in As $4p$ states. On the contrary, application of pressure suppresses exchange interactions. While Mn K $\beta$ emission spectra show a weak response of $3d$ states to pressure, clear As $4p$ band broadening (hole delocalization) is observed under pressure, ultimately leading to loss of ferromagnetism concomitant with a semiconductor to metal transition. The pressure response of As $4p$ and Mn $3d$ states is intimately connected with the evolution of the As-As interlayer distance and the geometry of the $\mathrm{MnA}{\mathrm{s}}_4$ tetrahedral units, which we probed with x-ray diffraction. Our results indicate that hole doping increases the degree of covalency between the anion (As) $p$ states and cation (Mn) $d$ states in the $\mathrm{MnA}{\mathrm{s}}_4$ tetrahedron, a crucial ingredient to promote indirect exchange interactions between Mn dopants and high $T\mathrm{c}$ ferromagnetism. The instability of ferromagnetism and semiconducting states against pressure is mainly dictated by delocalization of anion $p$ states.

The hallmark of a skyrmion crystal (SkX) is the topological Hall effect (THE). In this article we predict and explain an unconventional behavior of the topological Hall conductivity in SkXs. In simple terms, the spin texture of the skyrmions causes an inhomogeneous emergent magnetic field whose associated Lorentz force acts on the electrons. By making the emergent field homogeneous, the THE is mapped onto the quantum Hall effect (QHE). Consequently, each electronic band of the SkX is assigned to a Landau level. This correspondence of THE and QHE allows us to explain the unconventional behavior of the THE of electrons in SkXs. For example, a skyrmion crystal on a triangular lattice exhibits a quantized topological Hall conductivity with steps of $2·e^2/h$ below and with steps of $1·e^2/h$ above the van Hove singularity. On top of this, the conductivity shows a prominent sign change $\mathit{at}$ the van Hove singularity. These unconventional features are deeply connected to the topology of the structural lattice.

We study spin-wave excitations in a circular ferromagnetic nanodot in different inhomogeneous, topologically nontrivial magnetization states, specifically, vortex and skyrmion states. Gradual change in the strength of the out-of-plane magnetic anisotropy and the Dzyaloshinskii-Moriya exchange interaction leads to continuous phase transitions between different stable magnetic configurations and allows for mapping of dynamic spin modes in and between the vortex, Bloch-type skyrmion, and Néel-type skyrmion states. Our study elucidates the connections between gyrotropic modes, azimuthal spin waves, and breathing modes in these various stable magnetization states and helps us to understand the rich spin excitation spectrum on the skyrmion background.

We have investigated the magnetic ground state of CuFeAs and CuFeSb by means of ${}^{57}\mathrm{Fe}$-Mössbauer spectroscopy, muon spin rotation/relaxation $\left(\mu \mathrm{SR}\right)$, neutron diffraction, and electronic structure calculations. Both materials share the 111-LiFeAs crystal structure and are closely related to the class of iron-based superconductors. In both materials there is a considerable occupancy of the Cu site by Fe, which leads to ferromagnetic moments, which are magnetically strongly coupled to the regular Fe site magnetism. Our study shows that CuFeAs is close to an antiferromagnetic instability, whereas a ferromagnetic ground state is observed in CuFeSb, supporting theoretical models of anion height driven magnetism.

Strong coupling in cavity-magnon systems has shown great potential for use in spintronics and information processing technologies due to the low damping rates and long coherence times. Although such systems are conceptually similar to those coupled by magnon-polaritons (MPs), the link between magnon-cavity coupling and MPs has not been explicitly defined. In this work we establish such a connection by studying the frequency-wave-vector dispersion of a strongly coupled magnon-cavity system, using a height-adjustable microwave cavity, and by modeling the observed behavior through the system's effective permeability. A polariton gap between the upper and lower coupled modes of the magnon-cavity system is defined, and is seen to be dependent on the system's effective filling factor. This gap is equal to the MP polariton gap in the limit where filling factor = 1, corresponding to the removal of the microwave cavity. Thus our work clarifies the connection between magnon-cavity and MP coupling, improving our understanding of magnon-photon interactions in coupled systems.

Despite the crucial role of interfacial perpendicular magnetic anisotropy in a Co(Fe)/MgO-based magnetic tunnel junction, the underlying mechanism is still being debated. Here, we report an anatomical study of the oxygen and Mg effect on $\mathrm{Pt}/\mathrm{Co}$ bilayers through repeated in situ anomalous Hall effect measurements, controlled oxygen exposure, and Mg deposition in an ultrahigh vacuum system. We found that chemisorbed oxygen not only quenches the effective magnetic moment of the Co surface layer, but also softens its magnetic anisotropy. However, a subsequent Mg dusting on the oxygen preexposed $\mathrm{Pt}/\mathrm{Co}$ surface can recover the magnetic anisotropy. The ab initio calculations on the exchange splitting and orbital hybridization near the Fermi level give a clear physical explanation of the experimental observations. Our results suggest that the Co(Fe)-O-$M$ bond plays a more important role than the widely perceived Co(Fe)-O bond does in realizing interfacial perpendicular magnetic anisotropy in Co(Fe)/MgO heterostructures.

We report about the anomalous Hall effect in $4f 3d$ metallic alloys measured using terahertz time-domain spectroscopy. In this way, we succeeded in revealing ultrafast dynamics of the anomalous Hall effect which accompanies the sub-100-ps optically induced magnetization reversal in a GdFeCo alloy. The experiments demonstrate the ability to control currents at terahertz frequencies in spintronic devices magnetically and ultrafast.